New Jersey Democratic Rep. Josh Gottheimer told CNBC that he has a solution for high-tax states that will be hurt by the new cap on state and local (SALT) deductions — and he believes it will stand up to legal scrutiny.

The overhaul of the nation's tax code, signed into law late last year by President Donald Trump, limits the amount of SALT deductions to $10,000. Previously, there was no limit. New Jersey has some of the highest property taxes in the country.

"People would be able to give a charitable contribution to their towns, their municipalities and the towns can give a tax credit on people's property tax bills," Gottheimer said in an interview with "Power Lunch."

Gottheimer recently unveiled the proposal, along with New Jersey Gov.-elect Phil Murphy, Rep. Bill Pascrell, D-N.J., and several local mayors.

The idea is for local governments to establish or support funds that pay for local services like roads, bridges and police officers. Taxpayers can make voluntary contributions, for which they will get a tax credit.

Gottheimer believes the IRS code allows for such a move. In fact, 22 states already do a version of this and eight law professors just came out in support of the proposal, he said.

"The IRS has ruled on this, the municipality is allowed to give a tax credit for contributing to them," Gottheimer said.

An IRS spokesperson told CNBC it is the agency's policy to correspond directly with members of Congress regarding legislation and had no further comment.

However, Gottheimer conceded that more needs to be done to ease the tax burden, including getting expenditures under control.

"We've got to cut taxes. But why not claw back the dollars? We just faced a tax hike. I'm for looking for every single way to actually get those dollars back and cut our taxes."